Approximately spin-projected Hessian for broken symmetry method and stretching frequencies of F2 and singlet O2

An approximate spin projection (AP) method is applied to a second derivative of energy (Hessian) of the broken‐symmetry (BS) method in order to eliminate a spin contamination error. Stretching frequencies of F2 (X1 ∑ g+) and singlet molecular oxygen (a1Δg) are calculated by using the spin‐projected Hessian (AP Hessian). In case of F2 molecule, a potential curve of an unrestricted Hartree‐Fock (UHF) method does not have an energy minimum but the stretching frequency can be calculated by the AP UHF method. The difference in the calculated stretching frequencies between a restricted HF (RHF) and the AP UHF methods is 650–700 cm−1, and indicates that a static correlation correction is a crucial to consider the frequency. On the other hand, we cannot find a significant difference in calculated frequencies of RHF and AP‐BS HF in case of 1O2 molecule within the HF method. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009